A 48-kg box is being pushed a distance of 7.5 m across the floor by a force Upper POverscript right-arrow EndScripts whose magnitude is 185 N. The force Upper POverscript right-arrow EndScripts is parallel to the displacement of the box. The coefficient of kinetic friction is 0.23. Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force.
Two are easy :)
Force down = m g, does no work, no motion up or down
Force up from floor = m g, also does no work
The third is easy too
work done by input force = +185 * 7.5
= + 1388 Joules
Now the negative one, the friction force which is opposite to motion
F = - mu m g = - .23 * 48 * 9.81
= - 108 Newtons
Work = - 108 * 7.5 = -812 Joules
You put more in than the friction took out, so the box accelerates
To determine the work done on the box by each of the four forces, we need to calculate the work done by each force separately.
1. Work done by the applied force:
The work done by the applied force (the force pushing the box) can be calculated using the formula:
Work = Force x Displacement x cos(theta)
Here, the force (F) is 185 N, and the displacement (d) is 7.5 m. The angle (theta) between the force and displacement vectors is 0 degrees because they are parallel. Therefore, cos(theta) = 1.
Work = 185 N x 7.5 m x 1 = 1387.5 Joules
Since the applied force is in the same direction as the displacement, the work done by the applied force is positive.
2. Work done by the force of gravity:
The work done by the force of gravity can be calculated using the formula:
Work = Force x Displacement x cos(theta)
Here, the force of gravity (F) is the weight of the box, which can be calculated as the mass (48 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). The displacement (d) is 7.5 m. The angle (theta) between the force and displacement vectors is 180 degrees because they are in opposite directions. Therefore, cos(theta) = -1.
Work = - (48 kg x 9.8 m/s^2) x 7.5 m x (-1) = -3528 Joules
Since the force of gravity is in the opposite direction to the displacement, the work done by the force of gravity is negative.
3. Work done by the normal force:
The work done by the normal force is zero because the normal force is perpendicular to the displacement, and the cosine of 90 degrees is zero.
4. Work done by the force of friction:
The work done by the force of friction can be calculated using the formula:
Work = Force x Displacement x cos(theta)
Here, the force of friction (F) can be calculated using the formula:
F = coefficient of friction x normal force
The coefficient of kinetic friction is given as 0.23. The normal force is equal to the weight of the box (48 kg x 9.8 m/s^2). The displacement (d) is 7.5 m. The angle (theta) between the force and displacement vectors is 180 degrees because they are in opposite directions. Therefore, cos(theta) = -1.
F = 0.23 x (48 kg x 9.8 m/s^2) = 108.4224 N
Work = - (108.4224 N) x 7.5 m x (-1) = 811.6675 Joules
Since the force of friction is in the opposite direction to the displacement, the work done by the force of friction is negative.
In summary, the work done on the box by each force is as follows:
- Work done by the applied force: 1387.5 Joules (positive)
- Work done by the force of gravity: -3528 Joules (negative)
- Work done by the normal force: 0 Joules
- Work done by the force of friction: -811.6675 Joules (negative)